In this paper, I describe and analyze a novel pattern of secondary stress in Tohono O'odham. Tohono O'odham (formerly known as Papago) assigns primary stress to the first syllable in content words (Hale 1959; Saxton 1963; Hill and Zepeda 1992). Fieldwork by the author on Tohono O'odham shows that a word-final secondary stress is disallowed in monomorphemic words but is allowed in polymorphemic words. This descriptive generalization holds regardless of the morphological composition or the derivational history of the word. This appears to be a novel stress pattern in the world's languages; no similar pattern appears in either Halle and Vergnaud (1987) or Hayes (1995), two important typological works on metrical systems. Optimality theory (McCarthy and Prince 1993; Prince and Smolensky 1993) ranks constraints in a single hierarchy that evaluates both derived and underived words without a serial derivation. O'odham secondary stress is accounted for in this way by proposing the morpheme-to-stress principle, a constraint requiring that each morpheme be stressed. This is true, as long as rhythmic considerations against clashes and lapses are respected. The morpheme-to-stress principle provides an optimality-theoretic account of this interesting metrical asymmetry between derived and underived words in Tohono O'odham and offers an account of other types of morphological stress systems.